System and method for detection and tracking of targets

ABSTRACT

System and method for detection and tracking of targets, which in a preferred embodiment is based on the use of fractional Fourier transformation of time-domain signals to compute projections of the auto and cross ambiguity functions along arbitrary line segments. The efficient computational algorithms of the preferred embodiment are used to detect the position and estimate the velocity of signals, such as those encountered by active or passive sensor systems. Various applications of the proposed algorithm in the analysis of time-frequency domain signals are also disclosed.

This application claims priority of provisional application Ser. No.60/209,758 filed Jun. 6, 2000, which is incorporated herein byreference.

FIELD OF THE INVENTION

The present invention relates to active and passive sensor applications,and more particularly is directed to efficient systems and methods fordetection and tracking of one or more targets.

BACKGROUND OF THE INVENTION

Detection and tracking of targets by sensor systems have been thesubject matter of a large number of practical applications. Sensorsystems designed for this purpose may use propagating wave signals, suchas electromagnetic or acoustical signals. Some sensor systems, such asradar and active sonar systems, are designed to receive reflections of atransmitted signal generated by an appropriate conventional transmitter.This type of sensor systems will be referred to as active sensorsystems. In contrast with the active sensor systems, in many casessensor systems are designed to receive signals not generated by acooperating transmitter. Such sensor systems will be referred to next aspassive sensor systems.

Active sensor systems are generally used for detection of scatteringobjects that show great variation in size and type. In the presence of ascattering object, the transmitted signal arrives to the receivingsensor system with a certain time delay, which is related to the rangeof the scattering object (i.e., the distance to it). Also, if thescattering object is moving, the reflected signal exhibits a spectralshift that is known as a Doppler shift. The Doppler shift is related tothe relative velocity of the object with respect to the sensor system.In order to provide an example of a received signal in an active sensorsystem, a simulation has been conducted for a radar system thattransmits a phase-coded radar signal as shown in FIG. 1A. In thissimulation, the transmitted signal reflects back from an object, at a 12km range, which is moving with a velocity of 400 m/s towards the radarsystem. The reflected signal is received by the radar antenna anddown-converted by a conventional analog receiver system, such as shownin FIG. 4. The output of the analog receiver system is shown in FIG. 1B,where the effects of the object range and velocity are seen as a delayand an additional frequency modulation of the received signal,respectively. These two prominent effects of the received signal can bemore readily observable on the cross-ambiguity function of thetransmitted and received signals, which is defined as:

A _(r,s)(τ,ν)=∫r(t+τ/2)s*(t−τ/2)e ^(j2πvt) dt  (1.1)

where s(t) is the transmitted signal and r(t) is the received signal.For the transmitted and received signal pair shown in FIGS. 1A and 1B,respectively, the magnitude of the cross-ambiguity function isillustrated in FIG. 1C as a 3-Dimensional plot. In FIG. 1D, the contourplot of the same cross-ambiguity function is provided. Since it iseasier to visualize the structure, contour plots of the cross-ambiguityfunction are more commonly used in practice. As seen in FIG. 1D, thepeak of the cross-ambiguity function is located at the correspondingdelay and Doppler shift caused by the scattering object. This observedcorrespondence between the peak location of the cross-ambiguity functionon one hand, and the position and the velocity of the scattering objecton the other is a general relationship, which holds true in all caseswhere there is no or little noise at the receiver.

In the case of a noisy reception of the reflected signal, the peaklocation of the cross-ambiguity function still provides a reliableestimate of the delay and the Doppler shift caused by the scatteringobject [1]. Therefore, in accordance with the present invention it ispossible to detect the presence of a scattering object by finding thepeak locations of the cross-ambiguity function and comparing them withappropriately chosen threshold levels. Those peaks that exceed thethresholds can be identified as scattering objects, and the locations ofthe peaks will provide the corresponding delay and Doppler shiftinformation at the same time.

Although the use of the cross-ambiguity function for detection ofscattering objects and estimation of their corresponding delay andDoppler shifts is known in the prior art, this approach has only beenused in sophisticated sensor systems because of the high cost anddifficulty of implementation. Therefore, in most of the applicationswhere the cost is a critical issue, the sensor systems are designed todetect the presence of scattering objects and estimate either theirrange or their velocities, but not both. The main objective of thepresent invention in relation to active sensor systems is to provide anefficient and low-cost system and method that can reliably detectscattering objects and estimate both their delay and their Dopplershifts at the same time.

Passive sensor systems are generally used for the interception ofsignals emitted by transmitters that are not in cooperation with thesensor system, i.e., operate independently of it. Unlike the activesensor systems where the range and the velocity of the objects can beestimated from the reflected signals, passive sensor systems cannotdecide on the range and the velocity of the intercepted transmitterwithout extensive prior information about the transmitter. In passivereception, the main purpose is the detection of an existing transmitter.Once a transmitter is detected, its intercepted signal can be analyzedto obtain information about the type and purpose of the transmitter.This information generally plays a crucial role in determining what typeof action should be taken in the presence of the detected transmitter.FIG. 2A shows a frequency-modulated signal, which is an example of anintercepted signal by a passive sensor system. The instantaneousfrequency of this signal varies in time, as shown in FIG. 2C. Theintercepted signal is down-converted by a conventional analog receiversystem as shown, for example, in FIG. 4. The output of the analogreceiver system is shown in FIG. 2B, where synthetic noise is added tosimulate an actual noisy reception. As seen from FIG. 2B, the detectionof the signal can be a difficult task, especially for interceptedsignals that have low amplitudes. Therefore, in cases where thedetection of weaker signals in noise is extremely important, such as inearly warning applications, more sophisticated detection algorithms arerequired. Similar to the case of active sensor systems, in accordancewith the present invention reliable detection of signals in noise can beperformed in the ambiguity-function domain by computing theauto-ambiguity function of the down-converted received signal asfollows:

A _(r)(τ,ν)=∫r(t+τ/2)r*(t−τ/2)e ^(j2πvt) dt  (1.2)

where r(t) is the received signal. The noisy received signal is shown inFIG. 2C, and its corresponding auto-ambiguity function is shown in FIG.2D. As seen in FIG. 2D, the intercepted signal is easily detectable inthis plot. However, in practice the auto-ambiguity function approach isalmost never used in the detection of intercepted signals due to theassociated high cost and complexity. The main objective of the presentinvention in relation to the passive sensor systems is to provide anefficient and low-cost method and algorithm that makes use of theauto-ambiguity function for reliable detection and classification ofintercepted signals.

The interested reader is directed to the disclosure of the followingpublications, which are incorporated by reference for additionalbackground. Reference numerals used in the following descriptioncorrespond to the numbering in the listing below.

[1] P. M. Woodward, Probability and Information Theory, withApplications to Radar, New York: Pergamino Press Inc., 1953.

[2] V. Namias, “The fractional order Fourier transform and itsapplication to quantum Mechanics”, J. Inst. Math. Appl., vol. 25, pp.241-265, 1980.

[3] W. Lohmann and B. H. Soffer, “Relationships between the Radon-Wignerand fractional Fourier transforms”, J. Opt. Soc. Am. A, vol. 11, pp.1798-1801, 1994.

[4] A. K. Özdemir and O. Arikan, “Fast computation of the ambiguityfunction and the Wigner distribution on arbitrary line segments ”, IEEEtrans. Signal Process., October 1999.

[5] A. K. Özdemir and O. Arikan, “Efficient computation of the ambiguityfunction and the Wigner distribution on arbitrary line segments”, inProc. IEEE Int. Symp. Circuits and Systems, vol. IV, pp. 171-174, May1999.

[6] I. Raveh and D. Mendlovic, “New properties of the Radon transform ofthe cross-Wigner/ambiguity distribution function”, IEEE Trans. SignalProcess., vol. 47, no. 5, pp. 2077-2080, July 1999.

[7] D. Mendlovic and H. M. Ozaktas, “Fractional Fourier transforms andtheir optical implementation: I” J. Opt. Soc. Am. A, vol. 10, pp.1875-1881, 1993.

[8] H. M. Ozaktas and D. Mendlovic, “Fractional Fourier transforms andtheir optical implementation: I, J. Opt. Soc. Am. A, vol. 10, pp.2522-2531, 1993.

[9] H. M. Ozaktas, O. Arikan, M. A. Kutay and G. Bozdagi, “Digitalcomputation of the fractional Fourier transform”, IEEE Trans. SignalProcess., vol. 44, no. 9, pp. 2141-2150, September 1996.

[10] L. B. Almedia, “The fractional Fourier transform and time-frequencyRepresentations”, IEEE Trans. Signal Process., vol. 42, no. 11, pp.3084-3091, November 1994.

[11] L. Cohen, “Time-frequency distributions—A review”, Proc. IEEE, vol.77, no. 7 pp. 941-981, July 1989.

[12] A. Papoulis, The Fourier Integral and its Applications, McGraw-HillBook Company, Inc., 1962.

[13] G. H. Golub and C. F. Van Loan, Matrix Computations, Baltimore:John Hopkins University Press, 1996.

[14] P. W. East (ed.), Advanced ESM Technology, Microwave Exhibitionsand Publishers Ltd., 1988.

[15] V. G. Nebabib, Methods and Techniques of Radar Recognition, ArtechHouse, Inc., 1995.

[16] R. E. Blahut, W. Miller and Jr. C. H. Wilcox, Radar and Sonar,Springer-Verlag, vol. 32, 1991.

[17] R. E. Kalman, “A new approach to linear filtering and predictionproblems”, J. Basic Engineering, Trans. ASME Series D, vol. 82, pp.35-45, 1960.

[18] R. E. Kalman and R. S. Bucy, “New results in linear filtering andprediction theory”, J. Basic Engineering 83D, pp. 95-108, 1961.

[19] L. R. Rabiner, R. W. Schafer and C. M. Rader, “The chirpZ-transform algorithm and its applications”, Bell Syst. Tech. J., vol.48, pp. 1249-1292, May 1969.

Additional information is also provided in U.S. Pat. Nos. 5,760,732;5,657,022; 5,583,505; 5,548,157 and 5,457,462, which are incorporatedherein by reference.

SUMMARY OF THE INVENTION

The present invention is based on the simultaneous computation ofdistance and Doppler shift information using fast computation of theambiguity function and/or Wigner distribution of received signals alongon arbitrary line. By using the fractional Fourier transformation oftime domain signals, closed form expressions for arbitrary projectionsof their auto or cross ambiguity function are derived. By utilizingdiscretization of the obtained analytical expressions, efficientalgorithms are proposed in accordance to the present invention tocompute uniformly spaced samples of the Wigner distribution and theambiguity function located on arbitrary line segments. With repeated useof the proposed algorithms, in alternative embodiments of the invention,samples in the Wigner or ambiguity domain can be computed onnon-Cartesian sampling grids, such as polar grids, which are the naturalsampling grids of chirp-like signals. The ability to obtain samples ofthe Wigner distribution and ambiguity function over both rectangular andpolar grids is potentially useful in a wide variety of applicationareas, including time-frequency domain kernel design, multicomponentsignal analysis, time-frequency domain signal detection and particlelocation analysis in Fresnel holograms.

BRIEF DESCRIPTION OF THE DRAWINGS

The advantages of the present invention will become apparent from thefollowing description of the accompanying drawings. It is to beunderstood that the drawings are to be used for the purpose ofillustration only, and not as a definition of the invention.

FIG. 1 is an illustration for an active sensor application in accordancewith this invention, where

FIG. 1A shows the transmitted signal;

FIG. 1B illustrates the received signal;

FIG. 1C is a 3-dimensional plot of the cross-ambiguity function of thereceived and transmitted signals; and

FIG. D shows the 1-D contour plot of the cross-ambiguity function of thereceived and transmitted signals.

FIG. 2 is an illustration for a passive sensor application in accordancewith this invention, where

FIG. 2A shows the frequency-modulated signal intercepted by a passivesensor system;

FIG. 2B shows the instantaneous frequency of the intercepted signal;

FIG. 2C shows the down-converted received signal for an analog receiver;and

FIG. 2D illustrates the 3-dimensional plot of the auto-ambiguityfunction of the down-converted received signal.

FIG. 3 is a block diagram illustrating a general structure of a systemin accordance with the present invention using conventional receiver anddisplay subsystems.

FIG. 4 is a block diagram illustrating the structure of a conventionalanalog receiver subsystem used in accordance with the present invention,which down-converts the received signal to the baseband to provide theinphase and quadrature signal components.

FIG. 5 is a block diagram illustrating a processing configuration inaccordance with a first embodiment of the invention.

FIG. 6 is a block diagram illustrating a processing configuration inaccordance with a second embodiment of the invention.

FIG. 7 is a block diagram illustrating a processing configuration inaccordance with a third embodiment of the invention.

FIG. 8 is a detailed block diagram illustrating a processingconfiguration in an alternative embodiment of the invention.

FIG. 9 is a block diagram illustrating the preferred configuration of aprocessor in accordance with one embodiment of the invention.

FIG. 10 is a block diagram illustrating the preferred configuration ofanother processor in accordance with a second embodiment of theinvention.

FIG. 11 is a block diagram illustrating the preferred configuration of atracker subsystem in accordance with a preferred embodiment of theinvention.

FIG. 12 illustrates an optical hardware that can be used to compute thecontinuous fractional Fourier transformation in a specific embodiment ofthe present invention.

FIG. 13 illustrates the projection geometry for the magnitude squaredambiguity function used in a preferred embodiment of the presentinvention.

FIG. 14 is a plot that shows the 32.7 degree projection of the magnitudesquared cross-ambiguity function of the signals shown in FIG. 1A andFIG. 1B.

FIG. 15 is a plot that shows the 50.0 degree projection of the magnitudesquared auto-ambiguity function of the signal shown in FIG. 2C.

FIG. 16 is a plot which shows, as a function of the projection angle,the peak values of the projections of the magnitude squaredauto-ambiguity function of the signal shown in FIG. 1A.

FIG. 17 is a contour plot, which shows an overlay of the cross-ambiguityfunctions for two alternative transmission signals s₁(t) and s₂(t) withband-limited uniform clutter at the receiver.

FIG. 18 is a plot where

FIG. 18A shows the 60.0 degree projection of the magnitude squaredcross-ambiguity function of the signal s₁(t) and its correspondingreceived signal in clutter; and

FIG. 18B shows the 45.0 degree projection of the magnitude squaredcross-ambiguity function of the signal s₂(t) and its correspondingreceived signal in clutter.

FIG. 19 is an illustration of the basic idea used in accordance with thepresent invention for the detection of the range and radial speed of asingle scattering object by using only a single projection, where theindicated line segment corresponds to the potential locations of thecross-ambiguity function peak.

FIG. 20 is an illustration of the performance of the detection ideashown in FIG. 19 where

FIG. 20A shows the noisy received signal;

FIG. 20B shows the 50.0 degree projection of the magnitude squaredcross-ambiguity function of the received and transmitted signals;

FIG. 20C shows the computed samples of the cross-ambiguity function onthe line segment, that corresponds to the red colored line segment inFIG. 19.

FIG. 21 is an illustration of the basic idea used in accordance with thepresent invention for the detection of the range and radial speed of asingle scattering object by using two projections, where theintersection of the lines perpendicular to the projection lines andpassing through the respective peak locations of the projections providean estimate for the peak location of the cross-ambiguity function of thereceived and transmitted signals.

FIG. 22 is an illustration of the idea used in accordance with thepresent invention for the detection of the ranges and radial speeds oftwo scattering objects by using two projections; four line segmentscorrespond to the potential locations of the cross-ambiguity functionpeaks, so by computing samples of the cross-ambiguity function on theseline segments, close estimates of the actual peak locations can befound.

FIG. 23 is an illustration of the idea used in accordance with thepresent invention for the detection of the ranges and radial speeds oftwo scattering objects by using two projections where the detected peakson the projections are significantly different in their amplitudes. Asshown in this figure, the peak locations can be estimated as the markedintersection points.

FIG. 24 is an illustration of how useful the projection domain signatureused in accordance with the present invention for the classification ofintercepted pulse signals. In particular,

FIGS. 24A-C show three different pulse signals intercepted by a passivesensor system.

FIGS. 24D-F show the respective instantaneous frequency modulations oneach pulse signal.

FIGS. 24G-I show the respective auto-ambiguity functions of the receivedsignals.

FIGS. 24J-L show the respective projection domain signatures of thereceived signals.

FIG. 25 is an illustration of how useful the projection domain signatureis in the classification of intercepted continuous signals.

FIGS. 25A-C show three different continuous signals intercepted by apassive sensor system.

FIGS. 25D-F shows the respective instantaneous frequency modulations oneach signal.

FIGS. 25G-I illustrate the respective auto-ambiguity functions of thereceived signals.

FIGS. 25J-L show the respective projection domain signatures of thereceived signals.

FIG. 26 is an illustration of how the tracking information on thepreviously detected objects can be used in obtaining the peak locationsof the cross-ambiguity function. The figure shows the detection of theranges and radial speeds of two scattering objects by using a singleprojection. The tracking information enables the search for the peaks ofthe cross-ambiguity function to be conducted over short line segments.

FIG. 27 is an illustration of how the tracking information on thepreviously detected objects can be used in obtaining the peak locationsof the cross-ambiguity function. In the illustration, the detection ofthe ranges and radial speeds of two scattering objects by using twoprojections is shown. As illustrated, the tracking information enablesthe identification of the new position of the tracked object. Thisidentification eliminates L₂ and L₃, and identifies L₄ as the peaklocation, corresponding to a newly detected object.

FIG. 28 is a drawing illustrating an arbitrary line segment L_(A) onwhich samples of the cross-ambiguity function can be computedefficiently using a computational algorithm in a preferred embodiment ofthe present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The present invention can be implemented using the generalized structureshown in FIG. 3, where conventional receiver and display subsystems areused along with various processing components of the system of theinvention. This structure can be adapted to achieve the above mentionedgoals for both the active and passive sensor applications. In thefollowing sections, the preferred configuration for each of theembodiments of the invention are presented in detail.

The receiver 10 of the system generally functions to receive the inputsignals, convert them to baseband signals that are typically detected inquadrature channels, and finally to filter the output. A more detailedblock diagram of a receiver used in accordance with this invention isshown in FIG. 4, which illustrates a receiving sensor 100, localoscillator 110, the output of which multiplies the received signals inmultiplier 120. Additional components of the system include IF amplifier130 and two quadrature channels, using a sin(x)/cos(x) multiplicationand filtering operation, as known in the art.

Processor blocks 20 and 30 generally form signal frames for furtherprocessing, preferably including time scaling. Further, processors 20,30 compute various transformations of the input signal, which aredesigned to determine a time-frequency function of the (transmitted or)received signals and to detect peaks of the function, which areindicative of the presence of one or more targets, and their positionand velocity at any time.

Tracking system 40 generally tracks the position of identified targets,and further communicates with the processors in determining optimum timewindows, etc. Finally, display 50 shows output prameters to an operator.Individual blocks of the system are considered in more detail next.

A. The First System Processor

FIGS. 5, 8 and 9 illustrate to various level of detail the configurationand operation of the first processor subsystem used in accordance withthe preferred embodiment shown in FIG. 4. Like processing blocks inthese figures are likely labeled for convenience. Accordingly, tosimplify the presentation, the discussion next focuses on the preferredembodiment of the processor shown in FIG. 9. As shown, in 200 thereceived signal is first segmented into frames for further processing.For an analog receiver these frames can be constructed as:

{overscore (r)} _(i) =I(t+Δt _(i) +T _(i)/2)+jQ(t+Δt _(i) +T _(i)/2), −T_(i)/2≦t<T _(i)/2.  (1.3)

By choosing the frame positions Δt_(i)'s and the frame durations T_(i)'sproperly, the frames can be constructed as overlapping ornon-overlapping, as desired. For improved computational efficiency, inthe implementation of the preferred embodiments, the followingtime-scaled signals are used:

r _(i)(t)={overscore (r_(i))}( t/s _(c))  (1.4)

For a signal with approximate time duration T and band width B thepreferred scaling constant is given by [9]:

S _(c) ={square root over (B/T)}  (1.5)

For simplicity in the actual implementation, all of the constructedsignal frames can be scaled with the same scaling constant. In thiscase, T should be chosen as the approximate time duration of the signalframe with the longest duration. Different scaling can be used inalternative embodiments.

Similarly, in accordance with the present invention, for a digitalreceiver the time-scaled signal frames are constructed from theavailable samples of the received signal as: $\begin{matrix}\begin{matrix}{{r_{i}\lbrack n\rbrack} = \quad {r_{i}( {n/( {2\Delta \quad r} )} )}} \\{= \quad {{\overset{\_}{r}}_{i}( {nT}_{S} )}} \\{{= \quad {{I( {{nT}_{S} + {N_{O}T_{S}}} )} + {{jQ}( {{nT}_{S} + {N_{O}T_{S}}} )}}}, -} \\{\quad {{{T_{i}/2} \leq {nT}_{S} < {T_{i}/2}},}}\end{matrix} & (1.6)\end{matrix}$

where Δr is the square root of the time-bandwidth product TB of thesignal {overscore (r_(i))}(t),

T _(S)=1/(2B)

denotes the sampling interval used by the digital receiver, and N₀ isthe closest integer to

(Δt _(i) +T _(i)/2)/T _(s).

In the preferred embodiment shown in FIG. 9, following the formation ofthe signal frames, for each of the constructed signal frames, thecorresponding fractional Fourier transform is obtained in 210, 220. Thefractional Fourier transformation is a generalization of the ordinaryFourier transformation that can be interpreted as a rotation by an anglein the time-frequency plane [2]. If the receiver provides analogsignals, the following continuous fractional Fourier transformation isapplied to the constructed signal frame: $\begin{matrix}{{r_{i,a_{i_{j}}}(t)} = {{\{ {F^{a_{i_{j}}}r_{i}} \} (t)} = {\int{{B_{a_{i_{j}}}( {t,t^{\prime}} )}{r_{i}( t^{\prime} )}{t^{\prime}}}}}} & (1.7)\end{matrix}$

where α_(i) _(j) is the order of the fractional Fourier transformation,and B_(a_(i_(j)))(t, t^(′))

is the kernel of the transformation defined as: $\begin{matrix}{{{B_{a_{i_{j}}}( {t,t^{\prime}} )} = {A_{\varphi_{i_{j}}}{\exp \lbrack {j\quad \pi \quad ( {{t^{2}\cot \quad \varphi_{i_{j}}} - {2{tt}^{\prime}\csc \quad \varphi_{i_{j}}} + {t^{\prime 2}\cot \quad \varphi_{i_{j}}}} )} \rbrack}}},} & (1.8)\end{matrix}$

where the transformation angle,ϕ_(i  j) = a_(i  j) × π/2, and  the  scaling  constant  A_(φ_(i_(j)))

is defined as: $\begin{matrix}{{A_{\varphi_{i_{j}}} = \frac{\exp ( {{{- j}\quad {{{\pi sgn}( {\sin \quad \varphi_{i_{j}}} )}/4}} + {j\quad {\varphi_{i_{j}}/2}}} )}{{{\sin \quad \varphi_{i_{j}}}}^{1/2}}},} & (1.9)\end{matrix}$

If the order α_(i) _(j) is chosen as 1, the fractional Fouriertransformation corresponds to the ordinary Fourier transformation.Continuous fractional Fourier transformation has very importantrelationships to both the ambiguity function and the Wigner distribution[3], [4], [5], [6]. The above-given form of the fractional Fouriertransformation can be computed in a preferred embodiment by using anappropriate hardware, such as the one shown in FIG. 12, which consistsof a pair of CCD arrays and a lens located inbetween [7], [8]. In thepreferred embodiment shown in FIG. 9, one or more fractional Fouriertransformations 210, 220 are computed. The orders α_(i) _(j) of thefractional Fourier transformations are decided preferably prior to theactual implementation by taking into account the received signal andclutter properties. The details of the how these orders can be chosen inpractice are discussed below.

In the case of a digital receiver, several algorithms can be utilized toefficiently obtain close approximations to the uniformly spaced samplesof the continuous fractional Fourier transform. For completeness, suchan efficient computational algorithm is given in Appendix A [4], [5]. Byusing the tabulated algorithm, the following set of discrete fractionalFourier transformations are computed for each of the constructed signalframes: $\begin{matrix}{{r_{i,a_{i_{j}}}\lbrack n\rbrack} = \{ {\begin{matrix}{{\sum\limits_{n^{\prime}}{{B_{a_{i_{j}}}\lbrack {n,n^{\prime}} \rbrack}{r_{i}\lbrack n^{\prime} \rbrack}}},} & {{a_{i_{j}}} \in \lbrack {0.5,1.5} \rbrack} \\{{\sum\limits_{n^{\prime}}{{B_{({a_{i_{j}} - 1})}\lbrack {n,n^{\prime}} \rbrack}{R_{i}\lbrack n^{\prime} \rbrack}}},} & {{a_{i_{j}}} \in {\lbrack {0,0.5} )\bigcup( {1.5,2} )}}\end{matrix},} } & (1.10)\end{matrix}$

where r_(i)[n] is given in (1.6) and R_(i)[n] is the discrete Fouriertransform of r_(i)[n] given as $\begin{matrix}{{{R_{i}\lbrack n\rbrack} = {\frac{1}{2B}{\sum\limits_{n^{\prime}}{{r_{i}\lbrack n^{\prime} \rbrack}^{{- j}\quad \frac{\pi \quad {nn}^{\prime}}{2{({\Delta \quad r})}^{2}}}}}}},} & (1.11)\end{matrix}$

where Δr is the square root of the time-bandwith product TB of thesignal {overscore (r_(i))}(t). The kernel of the transformationB_(a_(i_(j)))[n, n^(′)]

is defined as: $\begin{matrix}{{{B_{a_{i_{j}}}\lbrack {n,n^{\prime}} \rbrack} = {\frac{1}{2\Delta \quad r}A_{\varphi_{i_{j}}}{\exp \lbrack {j\frac{\pi}{4( {\Delta \quad r} )^{2}}( {{n^{2}\cot \quad \varphi_{i_{j}}} - {2{nn}^{\prime}\csc \quad \varphi_{i_{j}}} + {n^{\prime 2}\cot \quad \varphi_{i_{j}}}} )} \rbrack}}},} & (1.12)\end{matrix}$

where the transformation angleφ_(i_(j)) = a_(i_(j))π/2, and  the  scaling  constant  A_(φ_(i_(j)))

are defined as in Eq. (1.9). The discrete fractional Fouriertransformation has very important relationships to the continuousfractional Fourier transformation, and it can be used to approximatesamples of the continuous transformation:r_(i, a_(i_(j)))[n] ≅ r_(i, a_(i_(j)))(n/(2Δ  r))[9].

The above-given form of the discrete fractional Fourier transformationcan be computed efficiently by using algorithms that make use of fastFourier transformation [9]. For completeness, an efficient computationalalgorithm is given in Appendix A [9]. In actual real-timeimplementations, such a fast computational algorithm preferably isprogrammed in an integrated chip. The orders of the discrete fractionalFourier transformations can be chosen as in the continuous case byinvestigating the properties of the received signal and clutter.

The preferred configuration of the first embodiment shown in FIG. 9 isdesigned for both the active and passive sensor systems. In the case ofactive sensor applications, S_(i) in block FIG. 9 is set to be thetransmitted signal delayed with T_(i)/2. In the case of passive sensorapplications, S_(i) in block FIG. 9 is set to be the i-th receivedsignal frame. Then, S_(i) is also transformed into multiple fractionalFourier domains. In the preferred configuration, the orders of thefractional Fourier transformations are chosen to be the same as theorders used in the fractional Fourier transformations applied on thereceived signal frame in 220. Therefore, in passive sensor applications,the fractional Fourier transformations of S_(i) are identical to thoseof r_(i). Hence, it is not necessary to compute the fractional Fouriertransformations of S_(i). In the case of active sensor applications witha digital receiver, such a computational efficiency can be achieved bycomputing the required fractional Fourier transformations on thetransmitted signal in advance, and storing the results in a digitalmemory to be retrieved when necessary.

The results of the computed fractional Fourier transformations arecomplex valued signals. In the following processing blocks 215, 225, bycomputing their squared magnitudes, they are converted to real valuedsignals as: $\begin{matrix}\begin{matrix}{{s_{i,a_{i_{j}},2}(t)} = {{s_{i,a_{i_{j}}}(t)}}^{2}} \\{{r_{i,a_{i_{j}},2}(t)} = {{{r_{i,a_{i_{j}}}(t)}}^{2}.}}\end{matrix} & (1.13)\end{matrix}$

Then, in blocks 230 the correlation between the obtained S_(i,α) _(ij) ,and y_(i,α) _(ij) ,2 is computed as: $\begin{matrix}\begin{matrix}{{c_{i_{j}}(\rho)} = \quad {{corr}\quad ( {{r_{i,a_{i_{j}},2}(\rho)},{s_{i,a_{i_{j}},2}(\rho)}} )}} \\{= \quad {\int{{r_{i,a_{i},2}( {\rho + t} )}{s_{i,a_{i},2}^{*}(t)}{t}}}} \\{= \quad {\int{{{r_{i,a_{i_{j}}}( {\rho + t} )}}^{2}{{s_{i,a_{i_{j}}}(t)}}^{2}{{t}.}}}}\end{matrix} & (1.14)\end{matrix}$

Finally, a standard detector is used in 240 on the obtained correlationresults to identify the presence of peaks above the expected noisefloor. Locations of identified peaks are used as part of the processingin the second processor 30, as shown in FIG. 3. The underlyingfundamental relationship between the identified peaks and the presenceof an object is investigated in detail below.

As mentioned above, the ambiguity function reveals the presence of anobject in both active and passive sensor applications. However, due tothe associated complexity in the implementation of the requiredprocessing, detection on the ambiguity domain is rarely used inpractice. In this patent application, an alternative method of detectionof an object in the ambiguity domain is proposed. In this new approach,projections of the magnitude squared ambiguity function are used todetect the presence of an object. These projections are defined as:$\begin{matrix}{{{P_{r_{i},s_{i}}( {\rho,\varphi_{i_{j}}} )} = {\int{{{A_{r_{i},s_{i}}( {{{\rho \quad \cos \quad \varphi_{i_{j}}} - {u\quad \sin \quad \varphi_{i_{j}}}},{{\rho \quad \sin \quad \varphi_{i_{j}}} + {u\quad \cos \quad \varphi_{i_{j}}}}} )}}^{2}{u}}}},} & (1.15)\end{matrix}$

where ρ is the projection domain variable and φ_(i) _(j) is theprojection angle, as shown in FIG. 13. In order to demonstrate theeffectiveness of detecting objects in the projections of the magnitudesquared ambiguity function, the examples given in FIG. 1 and FIG. 2 areexamined next. For these two examples, the above defined projections arecomputed at projection angles 32.7° and 50.0°, respectively, and theircorresponding results are shown in FIG. 14 and FIG. 15. As seen from theobtained results, the presence of the object is readily detectable inthe computed projections. However, if these projections are computedbased on the given formula in Eq. (1.15), the required computation willbe even more complicated than the detection based on the ambiguityfunction domain. Therefore, in a preferred embodiment, an alternativemethod is presented for efficient computation of the requiredprojections.

A simplified form for the expression in Eq. (1.15) can be obtained byusing the following rotation property relating the ambiguity functionand the fractional Fourier transformation: $\begin{matrix}{{{A_{r_{i},s_{i}}( {{{\rho \quad \cos \quad \varphi_{i_{j}}} - {u\quad \sin \quad \varphi_{i_{j}}}},{{\rho \quad \sin \quad \varphi_{i_{j}}} + {u\quad \cos \quad \varphi_{i_{j}}}}} )} = {A_{r_{i,a_{i_{j}}},s_{i,a_{i_{j}}}}( {\rho,u} )}},} & (1.16)\end{matrix}$

where r_(i, a_(i_(j)))(t)  and  s_(i, a_(i_(j)))(t)

are the (α_(i) _(j) )^(th) order fractional Fourier transforms ofr_(i)(t) and S_(i)(t). This property of the fractional Fourier transformessentially means that the ambiguity function of the fractional Fouriertransformed signals A_(r_(i, a_(i_(j))), s_(i, a_(i_(j))))

is the same as the rotated ambiguity function A_(r) _(i) _(,S) _(i) ,with an angle of rotation equal to the transformation angle φ_(i) _(j) .Although this relationship is presented first time in this patentapplication, it can be obtained from the following well-known rotationproperty between the Wigner distribution and the fractional Fouriertransformation [3] $\begin{matrix}{{W_{r_{i}}( {{{\rho \quad \cos \quad \varphi_{i_{j}}} - {u\quad \sin \quad \varphi_{i_{j}}}},{{\rho \quad \sin \quad \varphi_{i_{j}}} + {u\quad \cos \quad \varphi_{i_{j}}}}} )} = {{W_{r_{i,a_{i_{j}}}}( {\rho,u} )}.}} & (1.17)\end{matrix}$

First, this well known rotation property for auto-Wigner distribution isgeneralized to the cross-Wigner distribution: $\begin{matrix}{{W_{r_{i},s_{i}}( {{{\rho \quad \cos \quad \varphi_{i_{j}}} - {u\quad \sin \quad \varphi_{i_{j}}}},{{\rho \quad \sin \quad \varphi_{i_{j}}} + {u\quad \cos \quad \varphi_{i_{j}}}}} )} = {{W_{r_{i,a_{i_{j}}},s_{i,a_{i_{j}}}}( {\rho,u} )}.}} & (1.18)\end{matrix}$

Then, by using the fact that there is a 2-D Fourier relation between thecross-ambiguity function and the cross-Wigner distribution [11], and byrecalling that 2-D Fourier transform of a rotated signal is the same asthe rotated 2-D Fourier transform of the original, the relation in Eq.(1.16) can be obtained.

Thus by using the rotation property given in Eq. (1.16), the projectiongiven in Eq. (1.15) can be written as $\begin{matrix}{{{P_{r_{i},s_{i}}( {\rho,\varphi_{i_{j}}} )} = {\int{{{A_{r_{i,a_{i_{j}}},s_{i,a_{i_{j}}}}( {\rho,u} )}}^{2}{u}}}},} & (1.19)\end{matrix}$

in terms of the fractional Fourier transformsr_(i, a_(i_(j)))(t)  and  s_(i, a_(i_(j)))(t).

Then, by using the definition of the cross-ambiguity function in Eq.(1.11), the projection given by Eq. (1.19) can be written as:$\begin{matrix}{{P_{r_{i},s_{i}}( {\rho,\varphi_{i_{j}}} )} = \quad {\int{\int{\int{{r_{i,a_{i_{j}}}( {t^{\prime} + {\rho/2}} )}{s_{i,a_{i_{j}}}^{*}( {t^{\prime} -} }}}}}} \\{ \quad {\rho/2} ){r_{i,a_{i_{j}}}^{*}( {t^{''} + {\rho/2}} )}{s_{i,a_{i_{j}}}( {t^{''} -} }} \\{ \quad {\rho/2} )^{{j2\pi}\quad {u{({t^{\prime}t^{''}})}}}{t^{\prime}}{t^{''}}{u}} \\{= \quad {\int{\int{{r_{i,a_{i_{j}}}( {t^{\prime} + {\rho/2}} )}s_{i,a_{i_{j}}}^{*}}}}} \\{\quad {( {t^{\prime} - {\rho/2}} ){r_{i,a_{i_{j}}}^{*}( {t^{''} + {\rho/2}} )}{s_{i,a_{i_{j}}}( {t^{''} -} }}} \\{{ \quad {\rho/2} ){\delta ( {t^{\prime} - t^{''}} )}{t^{\prime}}{t^{''}}},}\end{matrix}$

where δ(t) is the Dirac-delta function [12]. Then, by using the siftingproperty of the Dirac-delta function, the expression for the projectioncan be simplified into: $\begin{matrix}{{P_{r_{i},s_{i}}( {\rho,\varphi_{i_{j}}} )} = {\int{{{r_{\quad_{i,a_{i_{j}}}}( {t^{\prime} + {\rho/2}} )}}^{2}{{s_{i,a_{i_{j}}}( {t^{\prime} - {\rho/2}} )}}^{2}{{t^{\prime}}.}}}} & (1.21)\end{matrix}$

Finally, by changing the variable of integration with t+ρ/2, theexpression for the projection given by Eq. (1.21) can be expressed as:$\begin{matrix}\begin{matrix}{{P_{r_{i},s_{i}}( {\rho,\varphi_{i_{j}}} )} = \quad {\int{{{r_{i,a_{i_{j}}}( {t + \rho} )}}^{2}{{s_{i,a_{i_{j}}}(t)}}^{2}{t}}}} \\{= \quad {{{corr}( {{r_{i,a_{i_{j}},2}(\rho)},{s_{i,a_{i_{j}},2}(\rho)}} )}.}}\end{matrix} & (1.22)\end{matrix}$

In this final form, the required projection is the same as thecorrelation ofr_(i, a_(i_(j)), 2)(ρ)  and  s_(i, a_(i_(j)), 2)(ρ).

Thus, the computed correlation C_(i) _(j) (ρ) in Eq. (1.14) is thedesired projection P_(r) _(i) _(,S) _(i) (ρ,φ_(i) _(j) ). Therefore, byusing this relationship, in the preferred implementation of the firstprocessor 20 of the system, these projections are obtained veryefficiently. Similarly, for a digital receiver, the required projectionscan be approximated as: $\begin{matrix}\begin{matrix}{{P_{r_{i},s_{i}}( {{m/( {2\Delta \quad r} )},\varphi_{i_{j}}} )} \cong \quad {{1/( {2\Delta \quad r} )}{\sum\limits_{n}{{r_{i,a_{i_{j}}}( ( {n +}  }}}}} \\{{ { \quad m )/( {2\Delta \quad r} )} )}^{2}{{s_{i,a_{i_{j}}}( {n/( {2\Delta \quad r} )} )}}^{2}} \\{\cong \quad {{1/( {2\Delta \quad r} )}{\sum\limits_{n}{{{r_{i,a_{i_{j}}}\lbrack {n + m} \rbrack}}^{2}{{s_{i,a_{i_{j}}}\lbrack n\rbrack}}^{2}}}}} \\{{= \quad {{1/( {2\Delta \quad r} )}{{corr}( {{{r_{i,a_{i_{j}}}\lbrack m\rbrack}}^{2},{{s_{i,a_{i_{j}}}\lbrack m\rbrack}}^{2}} )}}},}\end{matrix} & (1.23)\end{matrix}$

where r_(i,α) _(i) _(j) [n] and S_(i,α) _(i) _(j) [n] are the discretefractional Fourier transformations given by Eq. (1.10).

In actual implementation of the above detailed detection method, thechoice of the projection angles, φ_(i) _(j) , should be consideredcarefully. In some active sensor applications, due to hardwarelimitations, a fixed signal waveform is chosen for transmission. Inthese applications, the projection angles can be chosen in a preferredembodiment by computing the projections of the magnitude squaredauto-ambiguity function of the time-scaled transmitted signal,|A_(S)(τ,ν)|², at various angles. Then, the decision on the projectionangles can be based on a plot of the peak values of the individualprojections as a function of the projection angle. To illustrate thisapproach, the signal waveform shown in FIG. 2A is chosen as an example.The corresponding plot of the peak values of the individual projectionsas a function of the projection angle is shown in FIG. 16. Then for thisexample, angles φ₁=32.7° and φ₂=147.3°, where the largest peaks arelocated, can be determined on as the two projection angles to be used inthe preferred structure of the processor 20 of the system of thisinvention.

In some active sensor applications, the transmitted signal waveform canbe designed to obtain an improved performance in a given operationalenvironment. In the presence of a statistical description of the clutterand noise at the receiver, the transmitted signal can be designed sothat its computed projections in the preferred structure of the firstembodiment have more reliable detection performance. For instance, ifthe clutter has a uniform distribution in the shaded area shown in FIG.17, then signal s₁ provides better detection performance than signal s₂.This is because the shown projection for s₁ in FIG. 18A has less clutteraccumulation than the shown projection for s₂ in FIG. 18B. As seen fromthis example, the performance of the projection-based detection methodcan be improved considerably by a careful consideration of theoperational environment in the signal design phase.

B. Second System Processor

FIGS. 5 and 10 illustrate in block diagram form the structure andoperation of system processor 30 used in a preferred embodiment of theinvention. Again, like processing blocks are labeled with like referencenumerals. Focusing on FIG. 10, a block diagram illustrating thepreferred configuration of the second processor is shown. Thisembodiment of the invention is also designed for both the active andpassive sensor applications. In the case of active sensor applications,the second preferred embodiment provides estimates on the delays andDoppler shifts of the detected scattering objects. In the case ofpassive sensor applications, the second preferred embodiment providesestimates on the intercepted signal parameters. In the followingdescription, details of the preferred embodiment are provided for bothcases.

As detailed in the previous section, in the preferred structure of thefirst processor to detect the presence of an object, single or multiplecorrelations can be computed. In the case of active sensor applications,the second processor is designed to estimate the delay and Doppler ofthe scattering objects. In the case of detection based on a singlecorrelation computation in the first processor, the delay and Dopplerestimates can be obtained by an implementation of the idea presented inFIG. 19 for the simple case of detection of only one scattering object.As detailed in the previous section, the computed correlation c_(i) _(j)(ρ) is the projection of the magnitude squared cross-ambiguity function|A_(r) _(i) _(,S) _(i) (τ,ν)|² at an angle φ_(i) _(j) . Therefore, asshown in FIG. 19, the peak location of the cross-ambiguity functionA_(r) _(i) _(,S) _(i) (τ,ν) is either on or very close to the line,which passes through the detected peak of the correlation at d_(i) ₁ andperpendicular to the line of projection. Thus, by computing samples ofthe A_(r) _(i) _(,S) _(i) (τ,ν) on this line and detecting the locationof the largest amplitude peak, a reliable estimate to the peak locationof the cross-ambiguity function A_(r) _(i) _(,S) _(i) (τ,ν) can beobtained in accordance with the invention. This idea can be implementedefficiently by using the fast computational algorithms presented in [4],[5]. For completeness, the fast computational algorithm presented in [4]is given in Appendix B. In actual real time implementations, such a fastcomputational algorithm can be programmed in an integrated chip. Toillustrate its performance, this method is simulated on the noisyreceived signal shown in FIG. 20A. Although there is significant noisein the received signal, the preferred structure of the first embodimentprovides a projection at an angle of 32.7° with a distinct peak as shownin FIG. 20B. In FIG. 20C, the computed samples of the A_(r) _(i) _(,S)_(i) (τ,ν) are shown. As seen from the obtained samples, the peaklocation of the A_(r) _(i) _(,S) _(i) (τ, ν) can be identified easily.Once the peak location of the A_(r) _(i) _(,s) _(i) (τ,v) is estimated,estimates for the delay and Doppler shifts of the detected object areobtained in a preferred embodiment as:

{overscore ({circumflex over (τ)})}_(i)={circumflex over (τ)}_(i) /S_(c) +Δt _(i)

{overscore ({circumflex over (ν)})} _(i) ={circumflex over (ν)} _(i) S_(c),  (1.24)

where S_(c) is the time-scaling constant defined in Eq. (1.5) and{circumflex over ({overscore (τ)})}_(i), {circumflex over ({overscore(n)})}_(i) are the delay and Doppler shift estimates for the targetobject in the original uncaged coordinates. In this particular example,the actual and estimated delays are

{overscore (τ)}_(i)=8.0×10⁻⁵ S

and

{overscore ({circumflex over (τ)})}_(i)=7.99×10⁻⁵ S,

respectively; and the actual and estimated Doppler shifts are

{overscore (v)}_(i)=2.67×10⁵ Hz

and

{overscore ({circumflex over (ν)})}_(i)=2.60×10⁵ Hz,

respectively. As seen from this example, very accurate estimates forboth the delay and Doppler can be obtained using the method of thepresent invention.

When more than one correlation are computed in the first processor, thedelay and Doppler estimates can still be obtained by using the methodpresented for the single correlation case detailed above. This methodcan be implemented for the individual correlations yielding a set ofdetection results. Then, these detection results can be sorted toidentify distinct scattering objects. The detection resultscorresponding to the same scattering object can be averaged to obtainmore reliable estimates. In the case of multiple correlationcomputations in the first processor, another alternative method can beused, which is based on the idea shown in FIG. 21. For simplicity, inthis figure the case of two correlation results corresponding to asingle scattering object is shown. As seen from this figure, the lines,which are perpendicular to the projection lines and passing through therespective detected peak locations, either intersect or get very closeat the peak location of the A_(r) _(i) _(,S) _(i) (τ,ν). Therefore, inthe case of a single detection on individual correlations, the peaklocation of the A_(r) _(i) _(,S) _(i) (τ,ν) can be estimated by solvingthe following linear system of equations in the least squares sense[13]: $\begin{matrix}{{\begin{bmatrix}{\cos \quad \varphi_{i_{1}}} & {\sin \quad \varphi_{i_{1}}} \\\vdots & \vdots \\{\cos \quad \varphi_{i_{k}}} & {\sin \quad \varphi_{i_{k}}}\end{bmatrix}\begin{bmatrix}\tau_{i} \\v_{i}\end{bmatrix}} = {{\begin{bmatrix}d_{i_{1}} \\\vdots \\d_{i_{k}}\end{bmatrix}N_{i}z_{i}} = {d_{i}.}}} & (1.25)\end{matrix}$

The weighted least squares optimal solution to the above linear systemof equations can be obtained as: $\begin{matrix}\begin{matrix}{{\hat{z}}_{i} = {\lbrack {( {N_{i}^{H}W_{i}N_{i}} )^{- 1}N_{i}^{H}W_{i}} \rbrack d_{i}}} \\{{= {M_{i}d_{i}}},}\end{matrix} & \text{(1.26)}\end{matrix}$

where W_(i) is a the positive definite weight matrix, and the

{circumflex over (Z)}_(i)=[{circumflex over (τ)}_(i) {circumflex over(ν)}_(i)]^(T)

corresponds to the estimated peak location of the A_(r) _(i) _(,S) _(i)(τ,ν). If the projection angles are kept constant during the dataacquisition, the matrix M_(i) in Eq. (1.26) can be computed in advanceand stored in a digital memory to be retrieved when necessary. Once thepeak location of the A_(r) _(i) _(,S) _(i) (τ,ν) is estimated, theactual delay and Doppler shifts of the detected object is estimated byusing Eq. (1.24) given above.

In the case of multiple peaks detected on individual correlations, inaccordance with the invention the corresponding peak locations of theA_(r) _(i) _(,S) _(i) (τ,ν) can be found in many alternative methods. Tointroduce some of these alternatives, a simple case of detection of twoscattering objects on two different projections is shown in FIG. 22. Thepotential locations of the peaks in A_(r) _(i) _(,S) _(i) (τ,ν) are atthe four intersections shown in FIG. 22. The decision in the actuallocations can be based on computing values of A_(r) _(i) _(,s) _(i)(τ,ν) around these four intersection points by using the algorithm givenin Appendix B. This method is shown as part of the preferred structureof the second embodiment in FIG. 10. If there is a significantdifference between the magnitudes of the detected peaks on eachcorrelation, in accordance with a second alternative method, thelocation of the peaks in A_(r) _(i) _(,S) _(i) (τ,ν) can be estimated asthe intersection of those perpendicular lines which correspond to thesimilar magnitude peaks. The idea behind this method is illustrated inFIG. 23. Once the peak locations of the A_(r) _(i) _(,S) _(i) (τ,ν) areestimated, the actual delay and Doppler shifts of the detected objectsare estimated by using Eq. (1.24) given above. In a third alternative,the potential peak locations of the A_(r) _(i) _(,S) _(i) (τ,ν) can bereduced to a set of a few potential peak locations by using theinformation on the previously detected and tracked objects. More detailon this alternative method is presented in the description of the thirdpreferred embodiment of the invention.

In passive sensor applications, the embodiments of the second processorperform measurements on the intercepted signal and classify it based onthe obtained results. Some of the intercepted signals have shortduration, that are called pulse signals, while some of the interceptedsignals have very long duration, that are called continuous signals. Inthe referred structure of the second processor 30, measurements areperformed on the intercepted signal to determine its time of arrival,amplitude and duration. Since these measurements can be performed byusing well-known conventional methods, no further detail is presentedhere on these measurements. The interested reader is directed to thedisclosure in [14], [15], which are incorporated by reference. Forintercepted pulse signals, the measurements of time of arrival,amplitude, duration and pulse repetition intervals can be used toclassify an intercepted signal. However, the success of these type ofclassifiers is limited because these measurements alone do not providesufficient information on the modulation of an intercepted signal.Furthermore, for intercepted continuous signals, since pulse durationand pulse repetition interval cannot be measured, the modulationinformation plays an even greater role in the classification ofintercepted continuous signals.

In this patent application, a new method is proposed to obtain importantinformation on the modulation of an intercepted signal in real time. Toillustrate the idea, examples on both pulse and continuous signals areinvestigated here. Detection results on three different pulse signalsshown in FIGS. 24A-C are considered first. These three signals haveidentical values for their time of arrivals, amplitude and duration.Therefore, it is not possible to distinguish them from one another basedon these measurements alone. The computed auto-ambiguity functions ofthese three signals used in accordance with the present invention areshown in FIGS. 24G-I, respectively. As seen from these auto-ambiguityfunctions, these three signals have significantly different ambiguitydomain characteristics. However, because of its computationalcomplexity, classification based on auto-ambiguity domaincharacteristics is not practical. On the other hand, the projections ofthe magnitude squared auto-ambiguity function, which is computedefficiently by using Eqns. (1.22) or (1.23), provides projection domainsignatures of these signals, which are shown in FIGS. 24J-L,respectively. Since the computed projection domain signaturessignificantly differ from each other, these three pulse signals can bedistinguished easily based on their projection domain signatures.

Similar conclusions can be drawn from the examination of the threedifferent continuous signals shown in FIGS. 25A-C. These three signalshave identical values for their amplitude and center frequency of theirmodulation. Therefore, it is not possible to distinguish them from oneanother based on these measurements alone. The computed auto-ambiguityfunctions of these three signals are shown in FIGS. 25G-I, respectively.In this computation the same length frames are used for each signal, andthe frame length is chosen as approximately the period of modulation.For more noisy received signals, the frame length can be chosen largerfor better detection and classification performance. As seen from theseauto-ambiguity functions, these three signals have significantlydifferent ambiguity domain characteristics. However, because of itscomputational complexity, classification based on auto-ambiguity domaincharacteristics is not practical. On the other hand, the projections ofthe magnitude squared auto-ambiguity function, which are computedefficiently by using Eqns. (1.22) or (1.23), provides projection domainsignatures of these signals shown in FIGS. 25J-L, respectively. Sincethe computed projection domain signatures differ significantly from eachother, these three continuous signals can be distinguished easily basedon their projection domain signatures.

In the preferred structure of the second processor, this classificationmethod is implemented as follows. In advance of the actual operation,the projection domain signatures of the signals that may be interceptedin the operational environment, and are computed over a dense samplinggrid. Based on a detailed study of these signatures, a few samples outof each signature are chosen as the critical set of samples. For eachsignature, most of these critical samples can be chosen around the peaklocations of the respective signature. Then, the obtained criticalsamples are stored in a digital memory to be retrieved when necessary.This reduction in the number of samples in each signal signature to afew critical ones, provides significant saving in the computation of therequired projections. During the actual operation, the projectionscorresponding to the critical samples are computed by using the fastcomputational algorithm presented in the detailed description of thefirst processor. Next, the obtained projections are compared with a setof stored signal signatures to find a matching one. If there is a match,the matching signal type is reported to the third processor of thesystem of the invention, which keeps track of the active transmitters.If no match is found, the signature of the intercepted signal istransferred to the tracker 40 to be stored for future analysis.

C. The System Tracker

FIG. 11 is a block diagram illustrating the preferred configuration of atracker 40 used in accordance with the present invention. The tracker isalso designed for both the active and passive sensor applications. Inactive sensor applications, the tracker keeps a list of the detectedobjects, where the delay and Doppler shift caused by individual objectsare recorded. In addition to the delay and Doppler shift information,when they are available, the motion direction of the objects should alsobe recorded. If an object in the list could not be detected by theactive sensor system in the most recent searches, it is removed from theactive list of objects. For each of the objects in the active list, thetracker analyzes the available information on the object and providesestimates for its future delay, Doppler shift and direction. Kalmanfiltering is a well-known technique that can be used to provide theseestimates [17], [18]. These estimates are used to shorten the processingtime in the first and second processor of the invention as detailedbelow.

The tracker reports the obtained estimates of the delay and Dopplershift caused by individual scattering objects as well as theirdirections to both the first and second processor used in the system ofthe invention. In the first processor this information is used in theconstruction of the received signal frames. In the preferred way, shortframes are constructed around the expected delays of the scatteringobjects whose estimated directions are very close to the current searchdirection of the sensor system. In this way, the likelihood of havingreflections from multiple objects in a received signal frame is keptlow. Furthermore, for those signal frames that are around the expecteddelays of the tracked objects, the detection thresholds used in thefirst embodiment can be adjusted for reliable detection of the trackedobjects. In other signal frames, which do not contain expectedreflections of the tracked objects, the search for new scatteringobjects are conducted as detailed in the above sections.

In the second processor, the information reported by the tracker is usedto estimate the delays and Doppler shifts corresponding to the trackedobjects. The available estimates of the tracker can be utilized in allthe alternative estimation methods presented in the detailed descriptionof the second processor. In the case of a single correlation computationin the first embodiment, the search for the cross-ambiguity functionpeaks can be conducted over short line segments whose centers are closeto the reported delay and Doppler shifts of the tracked objects. Thisidea is illustrated in FIG. 26.

FIG. 27. Since shorter line segments are used, less computation isrequired in the digital computation of cross-ambiguity function slicesby using the algorithm given in Appendix B. In the case of multiplescattering objects detected on multiple correlations, the potentiallocations of the peaks in A_(r) _(i) _(,S) _(i) (τ,ν) can be reduced byusing the reported tracked objects. To illustrate how the availableinformation on the tracked objects can be used to reduce the number ofpotential peak locations, an example case is shown in FIG. 27. As shownin this figure, there are four possible peak locations for the detectedobjects. The reported delay and Doppler shift estimates of the trackedobject shown in this figure can be used to identify actual peaklocations as follows. Among the four possible peak locations the closestone L₁ to the reported peak location is identified as an actual peaklocation. This identification eliminates the two other possible peaklocations (shown as L₂ and L₃ in the figure) and identifies the fourthone (shown as L₄ in the figure) as the peak location, corresponding to anewly detected object.

In passive sensor applications, the tracker keeps a list of theintercepted transmitters and their measured parameters by the secondprocessor. These parameters include the computed projection domainsignature, time of arrival, amplitude and duration of the interceptedsignal, as well as the direction of the intercepted signal and theoperation frequency interval of the receiver system. According to thecurrent search direction and frequency interval, the tracker reports theappropriate subset of active transmitters in this list to both the firstand second processors of the invention. Furthermore, the trackercontrols the operations performed in the first and second processor forefficient use of the available resources. In the preferred structure ofthe first processor, a set of projections given in Eq. (1.22) or Eq.(1.23) is computed at the projection angles dictated by the tracker. Theobtained projections are reported to the second processor. In thepreferred structure of the second processor, further measurements areperformed on the intercepted signal to determine its time of arrival,amplitude and duration. Based on the obtained information on theintercepted signal, a comparison of the intercepted signal is made withthe set of signals chosen by the tracker. If there is a match found, thematching signal type is reported to the third processor (the tracker) ofthe invention, which keeps track of the active transmitters. If there isno match found, the signature of the intercepted signal is compared witha larger set of previously stored signal signatures. If there is a matchfound in this second round of search, the matching signal is reported tothe tracker to be added to the active list of transmitters. However, ifthere is no match found even in this second round of search, theintercepted signal is transferred to the tracker to be stored for futureanalysis.

The foregoing description of the preferred embodiments of the presentinvention has been presented for purposes of illustration anddescription. It is not intended to be exhaustive nor to limit theinvention to the precise form disclosed. Many modifications andvariations will be apparent to those skilled in the art. The embodimentswere chosen and described in order to best explain the principles of theinvention and its practical applications, thereby enabling othersskilled in the art to understand the invention. Various embodiments andmodifications that are suited to a particular use are contemplated. Itis intended that the scope of the invention be defined by theaccompanying claims and their equivalents.

What is claimed is:
 1. A method for generating data for locatingreflecting objects, comprising the steps of: receiving signals r(t)reflected from at least one object; processing the received signals andsignals s(t) transmitted to the at least one object to compute a1-dimensional projection of the cross ambiguity function associated withthe received and transmitted signals; and estimating a signal delay andDoppler shift associated with the at least one object from the computedprojection.
 2. The method of claim 1, wherein the 1-dimensionalprojection is selected on the basis of the peaks of the cross ambiguityfunction.
 3. The method of claim 1, wherein the orientation of theprojection line is pre-determined on the basis of the auto ambiguityfunction of the transmitted signals s(t).
 4. The method of claim 1,wherein the received signals are continuous waveform signals.
 5. Themethod of claim 1, wherein the received signals are discrete-timesignals.
 6. The method of claim 1, wherein signals from two or moreobjects are received.
 7. The method of claim 6 wherein signal delay andDoppler shift associated with the two or more objects are estimated froma single computed projection.
 8. The method of claim 6 wherein signaldelay and Doppler shift associated with the two or more objects areestimated from two computed projections.
 9. The method of claim 1,further comprising the step of tracking the location and velocity of theat least one object over a period of time.
 10. A system for generatingdata for locating reflecting objects, comprising: means for receivingsignals r(t) reflected from at least one object; means for processingthe received signals r(t) and signals s(t) transmitted to the at leastone object to compute a 1-dimensional projection of the cross ambiguityfunction associated with the received and transmitted signals; and meansfor estimating a signal delay and Doppler shift associated with the atleast one object from the computed projection.
 11. The system of claim10 further comprising means for transmitting the signals s(t) to the atleast one object.
 12. The system of claim 10 further comprising meansfor computing the peaks of the cross ambiguity function.
 13. The systemof claim 12, wherein the 1-dimensional projection is selected on thebasis of the peaks of the computed cross ambiguity function.
 14. Thesystem of claim 12 further comprising means for estimating the level ofnoise in the signal.
 15. The system of claim 14 further comprising meansfor establishing a threshold value based on the estimated level ofnoise, and means for comparing peaks of the cross ambiguity function tothe established threshold.
 16. The system of claim 10 further comprisingmeans for computing the auto ambiguity function of the transmittedsignals s(t), and wherein the orientation of the projection line isdetermined on the basis of the computed auto ambiguity function.
 17. Thesystem of claim 10 further comprising tracking means for tracking theposition of identified objects.
 18. The system of claim 17, wherein saidtracking means communicates with the means for receiving signals and themeans for processing to determine optimum time intervals for selectingtime windows in which the received signals are processed.
 19. The systemof claim 18 further comprising a display for displaying output to anoperator.
 20. The system of claim 10 further comprising memory forstoring 1-D projection signatures in the auto ambiguity function domainof one or more signals of interest.
 21. The system of claim 20 furthercomprising means for comparing stored 1-D projection signatures with 1-Dprojections of an ambiguity function associated with the receivedsignals.
 22. The system of claim 21 further comprising means fordetermining properties of the received signals based on the comparisonwith stored 1-D projection signatures.
 23. The system of claim 10further comprising means for computing two or more 1-D projection lines.24. The system of claim 23, wherein the computed two or more projectionlines are used to estimate a signal delay and Doppler shift associatedwith two or more objects.
 25. The system of claim 24, wherein theprocessing means comprises means for computing signal correlation. 26.The system of claim 10, wherein the processing means comprises means forcomputing fractional Fourier transformation.
 27. The system of claim 10further comprising time-scaling means.
 28. A software program productstored on a computer readable medium, adapted for execution by a digitalcomputer, comprising: a software program module on said medium, whichcauses said computer to process digitized signals r(t) carryinginformation about properties of at least one object and to compute a 1-Dprojection along arbitrary line of an ambiguity function associated withthe digitized signals; and a software program module on said medium,which causes said computer to estimate a signal delay and Doppler shiftassociated with the at least one object from the computed projection.29. The software product of claim 28 further comprising a softwareprogram module for computing fractional Fourier transformation.
 30. Thesoftware program product of claim 28 further comprising a softwareprogram module for detecting peaks in a 2-D function.